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Dynamic Response of the Foundations Resting on a Two-layered Soil Underlain by a Rigid Layer

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Abstract

The present experimental investigations study the effect of layering over rigid base on the dynamic behavior of foundation under vertical mode of vibration. Model block vibration tests were conducted on a rigid surface footing resting on different layered soil systems underlain by rigid base. The rigid base was used to simulate the presence of bedrock. The tests were carried out in a pit of size 2.0 m × 2.0 m × 1.9 m (deep) using a concrete footing of size 0.4 m × 0.4 m × 0.1 m. A rotating mass type mechanical oscillator was used for inducing vibration in vertical direction. Different layered soil systems were prepared within the total depth of 1,200 mm over the rigid base. Locally available gravel and fly ash were used to form different layered soil systems. In total, 132 nos. model block vibration tests in vertical mode were conducted for different layering and loading combinations. The experimentally obtained results are also compared with the results obtained from the analysis by mass-spring-dashpot and equivalent half-space theory.

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Abbreviations

a o :

Dimensionless frequency ratio

B z :

Modified mass ratio

C U :

Uniformity coefficient

c :

Dashpot coefficient

c c :

Critical damping

D :

Damping factor (%)

D 10 :

Effective grain size

e :

Eccentricity of unbalanced mass

f nr :

Resonant frequency in Hz

F:

Nondimensional depth factor

F 1 and F 2 :

Modified displacement function

G :

Shear modulus of soil

G e :

Equivalent shear modulus of layered soil

h :

Thickness of layer

K :

Static stiffness of the soil mass

K e :

Equivalent stiffness

m :

Mass of the foundation or total vibrating mass (mass of foundation plus machine) in case of machine foundation

m e e :

Eccentric setting

r :

Radius of circular foundation

W :

Static weight

x :

Amplitude in vertical direction in mm

\( \dot{x} \) :

Velocity in vertical direction at any time

\( \ddot{x} \) :

Acceleration in vertical direction at any time

μ:

Poisson’s ratio

μ e :

Equivalent Poisson’s ratio

ρ:

Mass density of soil

θ:

Eccentric setting

ω:

Circular frequency of vibration

ω n :

Natural frequency of system

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Authors and Affiliations

  1. Engineers India Ltd, UG (Annex) Floor, Bikaji Cama Place, New Delhi, 110066, India

    A. Mandal

  2. Department of Civil Engineering, Indian Institute of Technology, Kharagpur, 721302, India

    D. K. Baidya & D. Roy

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  1. A. Mandal
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  2. D. K. Baidya
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  3. D. Roy
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Correspondence to A. Mandal.

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Mandal, A., Baidya, D.K. & Roy, D. Dynamic Response of the Foundations Resting on a Two-layered Soil Underlain by a Rigid Layer. Geotech Geol Eng 30, 775–786 (2012). https://doi.org/10.1007/s10706-012-9497-2

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